Estimation method/analysis strategy

Model fit assesses the degree to which the model that best represents the sample data actually reflects underlying theory (Hooper et al. 2008). Several procedures are undertaken to test the measurement properties of the model using latent variable and structural equation modelling. As an example, maximum likelihood estimation (MLE) is the most widely used approach due to the MLE's potential sensitivity to non-normal data (Hair et al., 1998; Kline, 1998; Byrne, 2001). There are also several model fit criteria commonly used: chi-square (χ²), goodness of fit index (GFI), adjusted goodness

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of fit index (AGFI), root mean square error of approximation (RMSEA), normed-fit index (NFI), comparative fit index (CFI) and Tucker Lewis index (TLI). These criteria are based on differences between the observed (original, S) and model-implied

(reproduced, E) correlation or covariance matrix (Schumacker and Lomax, 1996). In this study, RMSEA, NFI, CFI and TLI were adapted to evaluate the model fit.

4.10.5.1 Root mean square error of approximation (RMSEA)

One of the most widely used measures based on chi-square values is the root mean square error of approximation (RMSEA). The RMSEA measures attempt to correct for the tendency of the χ² goodness-of-fit test statistic to reject models with a large sample or a large number of observed variables (Hair et al. 2010). Thus, it better represents how well a model fits a population, not just a sample used for estimation (Hu and Bentler 1999). Browne and Cudeck (1993) also comment that RMSEA takes into account the error of approximation in the population. This discrepancy between observed and predicted values, as measured by the RMSEA, is expressed per degree of freedom, thus making the index sensitive to the number of estimated parameters in the model.

Subsequently, it explicitly tries to correct for both model complexity and sample size by including each in its computation.

Hair et al. (2010) suggest that lower RMSEA values indicate better fit. However, the question of what is a good value of RMSEA is debatable. Although Browne and Cudeck (1993) point that values less than 0.05 indicate good fit and values as high as 0.08 represent reasonable errors of approximation in the population, Golob (2003) claims a good model has a RMSEA value of less than 0.05. However, Hair et al. (2010) have confirmed that the value of RMSEA is between 0.03 and 0.08. In addition, an empirical examination of several measures found that the RMSEA was best suited for use in a confirmatory or competing models strategy as samples become larger, such as more than 500 respondents (Rigdon 1996).

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4.10.5.2 Normed-fit index (NFI)

The NFI is one of the original incremental fit indices. This statistic assesses the model by comparing the χ² value of the fitted model to the χ² value of the null model (Hooper et al. 2008). Values for this statistic range between 0 and 1.00, and a model with perfect fit would produce an NFI of 1. Although Bentler and Bonnet (1980) have recommended that values greater than 0.90 indicate a good fit, more recent suggestions state that cut- off criteria should be greater than 0.95 (Hu and Bentler 1999). A major drawback to this index is that it is sensitive to sample size, underestimating fit for samples less than 200 (Mulaik et al. 1989; Bentler 1990). Thus, this measure is not recommended to be solely relied on and rather one of the next two is used (Kline 2005; Kenny 2010).

4.10.5.3 Comparative fit index (CFI)

The comparative fit index (CFI) is a revised version of the NFI which takes into account sample size (Byrne 1998) so that it performs well even when sample size is small

(Bentler and Bonnet 1980; Hu and Bentler 1999; Tabachnick and Fidell 2007). Like the NFI, this statistic is derived from the comparison of a hypothesised model with the independence model. The values of CFI range between 0 and 1.00, with values closer to 1 indicating a good fit. Although a value of greater than 0.90 was initially considered representative of a well-fitting model (Bentler 1992), a revised cut-off value close to 0.95 has presently been advised by Hu and Bentler (1999) as indicative of a good fit. Fan et al.(1999) affirm that this index is one of the most widely used fit indices due to being one of the measures least affected by sample size.

4.10.5.4 Tucker Lewis index (TLI)

The TLI predates the CFI and it is conceptually similar in that it can be also used to compare alternative models or a proposed model against a null model (Tucker and Lewis 1973; Schumacker and Lomax 2004). Due to non-normed nature of the TLI, its values can fall below 0 or go above 1.00, thus a problem with the TLI is that it can be difficult to interpret (Byrne 1998). Typical models with values close to 1 indicate a good fit and models with a higher value suggest a better fit (Hair et al. 2010).

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Recommendations as low as 0.80 as a cut-off have been proffered, but Bentler and Hu (1999) have suggested greater than 0.95 as the threshold. In practice, the TLI and CFI generally provide very similar values (Hair et al. 2010).

4.11 Summary

In this chapter, the research methodology of the study is discussed. It starts with describing the basis of the research philosophy centred on the research design. This chapter then explains the procedures for conducting the research, which include the development of the questionnaire, the survey method adopted for data collection, data analysis procedures in terms of reliability, validity, confirmatory factor analysis and full SEM model followed by the estimation of the model using several model fit criteria.

The following chapter will present the empirical results of preliminary analysis, reliability analysis, validity analysis and the confirmatory factor analysis. Finally, structural results from the testing hypothesised model will be discussed.

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